Solar Physics

, Volume 137, Issue 1, pp 155–165 | Cite as

Fitting the sunspot cycles 10–21 by a modified F-distribution density function

  • W. Elling
  • H. Schwentek
Article

Abstract

It has been found that sunspot cycles 10–21, represented by quarterly mean values of Zürich sunspot number, can be suitably described by the F-distribution density function provided it is modified by introducing five characteristic parameters, in order to achieve an optimal fitting of each cycle. The average cycle calculated from cycles 10–21 has been used as a basis to forecast time and magnitude of the maximum of each cycle, as a function of various numbers of the first quarterly mean values in the beginning N = 8 to 16 quarters. The standard deviations at a 99% significance level calculated from the observed values depend on N, and vary from 1.6 to 1.1 quarters and 65 to 16 units of sunspot number. A rather sufficient forecast is obtained from N = 12 quarters (with inaccuracy of ± 1.5 quarters and ± 24 units); the forecast for cycle 22 yielded, for N = 12, the values t m = (15.4 ± 1.5) quarters (∼ 1990.I) and f(t m ) = (175 ±24 units).

Keywords

Standard Deviation Density Function Characteristic Parameter Sunspot Number Sunspot Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bevington, P. R.: 1969, Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York.Google Scholar
  2. Koeppe, P. and Hamann, C.: 1981, Markt und Technik 10, 60.Google Scholar
  3. Morris, M. J.: 1977, J.R. Statist. Soc. A140, 437.Google Scholar
  4. Pfanzagl, J.: 1978, Allgemeine Methodenlehre der Statistik II, de Gruyter, Berlin.Google Scholar
  5. Schwentek, H. and Elling, W.: 1984, Solar Phys. 93, 403.Google Scholar
  6. Solar Indices Bulletin: Monthly, National Geophysical Data Center, Solar-Terrestrial Physics Division (E/GC2), Boulder, Colorado 80303, U.S.A.Google Scholar
  7. Sunspot Bulletin: Waldmeier, M. and Zelenka, A.: to 1980, Swiss Federal Observatory, Zürich. Koeckelenbergh, A.: since 1980, Sunspot Index Data Center, Brussels, Belgium.Google Scholar
  8. Waldmeier, M.: 1935, Astron. Mitt. Eidg. Sternwarte Zürich, No. 133.Google Scholar
  9. Waldmeier, M.: 1961, The Sunspot-Activity in the Years 1610–1960, Verlag Schulthess, Zürich.Google Scholar
  10. Waldmeier, M.: 1968, Astron. Mitt. Eidg. Sternwarte Zürich, No. 286.Google Scholar
  11. Wilson, P. R., Donnelly, R. F., and Wilkinson, P.: 1990, Solar Phys. 125, 159.Google Scholar
  12. Wilson, R. M.: 1990, Solar Phys. 127, 199.Google Scholar

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • W. Elling
    • 1
  • H. Schwentek
    • 1
  1. 1.Max-Planck-Institut für AeronomieKatlenburg-LindauGermany

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